Purchase Solution

Triple Integrals : Changing the Order of Integration and Finding the Volume of a Wedge

Not what you're looking for?

Ask Custom Question

1. Using the integral ∫-1-->1 ∫x^2-->1 ∫0-->1-y dz dy dx
a) Sketch the region of integration.
Write the integral as an equivalent iterated integral in the order:
b) dy dz dx
c) dx dz dy
d) dz dx dy

2. Find the volume of a wedge cut from the cylinder x^2 +y^2 =1 by planes z=-y and z=0.
Please show me the process too.

Purchase this Solution

Solution Summary

Triple Integrals, Changing the Order of Integration and Finding the Volume of a Wedge are investigated. The solution is detailed and well presented.

Solution Preview

Hello and thank you for posting your question to Brainmass!

The solution is attached below (next to the paperclip icon) in two formats. one is in Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

The volume of integration can be seen in the figure below:

As you can see the z coordinate is bound between the plane z=0 on top and the line z=1-y on the top.
The y coordinate is bound by the plane y=1 from the right and the parabola y=x2 from the left.
x is simply bound between the planes x=±1 (front and back)

Conversion to dzdydx

We need to express y as functions of z and x, the limits of z as a function of x and the limits of x as constants.

Since the original limits of x are already constants, they stay the same.

The relation between y and z can be written as:

This is the upper limit of y. The original lower limit of y is x2. Since x is the last variable in the integration order, this can ...

Purchase this Solution


Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Probability Quiz

Some questions on probability